It's really hard to do this on an administrative level with the way that the price mechanism currently works. Prices are set at the margin, based on the most recent transaction. If I decide I'm willing to pay $72,000 for a single share of Microsoft stock, then Microsoft stock will momentarily be worth $72k, at least until the next transaction, and Bill Gates will be 1000x richer on paper. Similarly, if I turn around and sell that one share for 1 cent, Microsoft's value (and the net worth of everyone who owns it) will momentarily be cut by 7200x.

When do you assess the tax? If it's at any predictable interval of time, it opens the market up to massive manipulation schemes where people crash their own stocks to avoid paying taxes and bid up their rivals so they'll be forced to owe a massive tax bill.

You could I guess take an average over time to avoid the manipulation efforts, but then you still run into the issue many dot-com paper millionaires faced, where they were assessed a tax bill based on the paper value of their options but when it came time to pay it, the stock wasn't worth enough money to cover the taxes.

That's why we have the current system, where capital gains are taxed as income (though at a lower rate), but only when you sell them. That's the only time when you can put a fair value on the asset being sold, when it's convertible into the currency you actually plan to pay the taxes with.